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We show that a translation invariant implementation of min/max filtres along a line segment of slope in the form of an irreducible fraction $dy/dx$ can be achieved at the cost of $2+k$ min/max comparisons per image pixel, where $k=\max(|dx|,|dy|)$. Therefore, for a given slope, the computation time is constant and independent of the length of the line segment. We then present the notion of periodic moving histogram algorithm. This allows for a similar performance to be achieved in the more general case of rank filtres and rank-based morphological filtres. Applications to the filtering of thin nets and computation of both granulometries and orientation fields are detailed. Finally, two extensions are developed. The first deals with the decomposition of discrete disks and arbitrarily oriented discrete rectangles, while the second concerns min/max filtres along gray tone periodic line segments.

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Authors: SOILLE P, European Commission, Joint Research Centre, Space Applications Institute, Ispra (IT);TALBOT H, CSIRO-Mathematical and Information Sciences, Image Analysis Group, Sydney (AU)
Bibliographic Reference: An article published in: IEEE Transactions on Pattern Analysis and Machine Intelligence, November 2001 (Vol. 23, No. 11) pp. 1313-1329
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